Biomedical Engineering Reference
In-Depth Information
is.known.to.nine.digits'.accuracy.*.he.theory.that.light.has.a.wave.nature.with.a.deinite.wavelength.
very.accurately.explains.observed.interference.phenomena..However,.the.fact.that.individual.photons.
are. observed. in. photo. detection. experiments. is. not. explained. by. a. purely. wave. hypothesis. and. so. a.
quantum.interpretation.is.used..Planck's.constant.(ratio.of.photon.energy.to.wave.frequency).is.known.
to. approximately. 10. digits.. his. dual,. wave/particle,. nature. of. light. leaves. many. open. questions.. One.
question.to.ponder.is.what.is.the.nature.of.the.light.before.it.is.detected?.It.certainly.rigorously.obeys.a.
wave.theory.and.does.not.behave.like.a.particle..How.exactly.does.the.photon.interact.with.matter.and.
with.other.photons?.What.exactly.determines.a.“detection”.which.forces.the.photon.to.stop.acting.like.a.
wave.and.manifest.itself.as.a.particle?.hese.questions.are.the.subject.of.active.study.(and.much.specula-
tion).today..Although.fascinating.open.questions.remain,.the.present.theory.is.quite.practical.and.very.
accurate.for.application.in.instrument.building.and.performance.analysis.
1.2 Physical nature of Light
1.2.1
original concepts of Light
he.ancient.Greeks.had.the.hypothesis.(Empedocles,.ith.century.BC).that.human.vision.was.an.active.
event.initiated.by.the.eye..From.this.hypothesis.they.concluded.that.the.speed.of.light.was.ininite,.as.
one.could.see.arbitrarily.distant.objects.the.moment.the.eyelids.are.opened..In.the.1600s,.both.Galileo.
and.Newton.became.interested.in.light..Galileo.attempted.to.measure.the.speed.of.light.with.timing.
experiments.but.was.unsuccessful..It.was.successfully.measured.(to.within.30%).by.Olaf.Roemer.in.
1676.using.calculations.involving.the.eclipse.of.Jupiter's.moons..Isaac.Newton.posited.(
Hypothesis of
Light
,.1670).that.light.was.composed.of.“corpuscles,”.or.particles..his.became.the.popularly.accepted.
theory.for.over.a.century,.but.he.had.not.worked.out.the.corpuscle.theory.to.a.convincingly.quanti-
tative.level.and.had.trouble.explaining.interference.and.difraction..Christian.Huygens.developed.a.
wave.theory.of.light.(
Treatise on Light
,.1690).that.accounted.for.refraction,.difraction,.and.interfer-
ence..Huygens.wavelet.principle,.with.the.appropriate.intensity.normalizing.constants.subsequently.
derived,.forms.a.basic.wave.theory.that.now.accurately.predicts.all.the.wave.phenomena.of.light..It.is.
fascinating.to.note.that.Huygens'.construction.of.wave.optics.well.predates.the.electromagnetic.theory.
(Maxwell,.
Dynamical heory of the Electromagnetic Field
,.1865).where.the.equations.of.electricity.and.
magnetism.combine.to.predict.free-space.propagation.of.electromagnetic.waves..he.Maxwell.theory.
united.the.whole.spectrum.of.radiation.phenomena,.from.low.frequency.(radio).to.visible.light.to.hard.
X-rays.and.gamma.rays,.as.manifestations.of.electromagnetic.waves.diferentiated.only.by.wavelength.
A.particle.explanation.for.light.had.to.be.revived.(Einstein.1905).when.it.was.discovered.that.light.
interacts.with.matter.in.discrete.energy.packets.(Planck.1901)..As.it.is.not.easy.to.describe.light's.behav-
ior.in.terms.of.particles.(as.Newton.had.found),.an.uneasy.truce.was.reached.in.the.interpretation.of.
the.wave.function—the.electromagnetic.wave.in.the.case.of.the.photon—as.probability.amplitude..In.
this.interpretation,.the.squared.amplitude.of.the.wave.amplitude,.expressed.as.a.function.of.position,.is.
proportional.to.the.probability.that.the.particle.is.at.that.position..he.Copenhagen.interpretation.(Bohr.
and.Heisenberg.1924-1929),.as.this.came.to.be.called,.incorporated.the.wave.behavior.through.the.wave.
function.and.the.particle.behavior.through.the.interpretation.in.terms.of.probabilities.
1.2.2 Maxwell's equations and the Plane Wave Solutions
We.start.at.Maxwell's.equations,.a.basis.from.which.we.can.generate.the.classical.wave.concepts.includ-
ing.Huygens.theory..he.electric.and.magnetic.ields.obey
*
.
Since.1983,.the.speed.of.light.has.established.the.deinition.of.a.meter.through.the.deinition.
c
.=.299,792,458.m/s.
